ALBANY — President Obama and former President Bill Clinton are lending their political star power to an unlikely Democratic bid to win a special congressional election in an area that’s been a Republican bastion for more than a century.

The Nov. 3 contest in upstate New York’s 23rd Congressional District, a sprawling, 11-county area where registered Republicans outnumber Democrats by 45,000 voters, is shaping up as a test of a struggling GOP and a possible gauge of Obama’s coattails.

Obama, who carried the district by 5 percentage points in his landslide victory in New York last year, forced the special election when he named the incumbent, Republican John McHugh, his Army secretary. The president will host a fundraiser for the Democratic candidate, Bill Owens, on Tuesday in New York City.

In a fundraising e-mail for Owens, Clinton called the special election “bigger than just one candidate or one office . . . victory or defeat will also be seen as a referendum on President Obama’s agenda.”

Owens, 60, a Plattsburgh lawyer and retired Air Force captain, is one of three candidates competing for the seat. The others are Republican Dierdre Scozzafava, 49, a state assemblywoman, and Conservative candidate Doug Hoffman, 59, a businessman.

Hoffman’s spokesman, Rob Ryan, said the race will be a referendum on Obama’s first 10 months and on the future of the Republican Party.

Democrats see an opening in the traditionally Republican district because Scozzafava and Hoffman are splitting the conservative vote. An Oct. 15 survey by Siena College showed Owens with 33 percent, Scozzafava with 29 percent and Hoffman with 23 percent. The poll of 617 likely voters had a margin of error of plus or minus 3.9 percentage points.

Conservative groups such as The Club for Growth have endorsed Hoffman. Former House Speaker Newt Gingrich endorsed Scozzafava last week, in a move apparently aimed as shoring up the Republican’s support among conservatives.

Republicans have charged that Obama picked McHugh for the Army job because he viewed the 23rd District as vulnerable. Democrat Kirsten Gillibrand won the nearby 20th district, another longtime GOP stronghold, in 2006, and Democrat Scott Murphy won a close special election in March to hold the seat after Gillibrand was appointed to the U. S. Senate.

Whatever Obama’s motivations, McHugh, who represented the 23rd District since 1993, has the credentials for the Army job. He served on the House Armed Services Committee for years and worked with the oft-deployed 10th Mountain Division at Fort Drum, which is in the district.